aboutsummaryrefslogtreecommitdiff
path: root/docs
diff options
context:
space:
mode:
authorMarshall Lochbaum <mwlochbaum@gmail.com>2021-01-19 20:14:17 -0500
committerMarshall Lochbaum <mwlochbaum@gmail.com>2021-01-19 20:14:17 -0500
commit9265ab3508ec787e16027b82402d99d0f229de5a (patch)
tree86fc671b02783f6f2980e5a49c9047961c7aaaa7 /docs
parentbdc89692d3dd7675d08f706fc2bedcf903975ed5 (diff)
Clarify that inferred property errors only happen when the property is needed
Diffstat (limited to 'docs')
-rw-r--r--docs/spec/inferred.html1
1 files changed, 1 insertions, 0 deletions
diff --git a/docs/spec/inferred.html b/docs/spec/inferred.html
index e1d08a02..4e0ff4ae 100644
--- a/docs/spec/inferred.html
+++ b/docs/spec/inferred.html
@@ -7,6 +7,7 @@
<h1 id="specification-bqn-inferred-properties">Specification: BQN inferred properties</h1>
<p>BQN includes some simple deductive capabilities: detecting the type of empty array elements, and the Undo (<code><span class='Modifier'>⁼</span></code>) and Under (<code><span class='Modifier2'>⌾</span></code>) modifiers. These tasks are a kind of proof-based or constraint programming, and can never be solved completely (some instances will be undecidable) but can be solved in more instances by ever-more sophisticated algorithms. To allow implementers to develop more advanced implementations while offering some stability and portability to programmers, two kinds of specification are given here. First, constraints are given on the behavior of inferred properties. These are not exact and require some judgment on the part of the implementer. Second, behavior for common or useful cases is specified more precisely. Non-normative suggestions are also given as a reference for implementers.</p>
<p>For the specified cases, the given functions and modifiers refer to those particular representations. It is not necessary to detect equivalent representations, for example to reduce <code><span class='Paren'>(</span><span class='Function'>+-×</span><span class='Paren'>)</span><span class='Modifier'>⁼</span></code> to <code><span class='Function'>∨</span><span class='Modifier'>⁼</span></code>. However, it is necessary to identify computed functions and modifiers: for example <code><span class='Function'>F</span><span class='Modifier'>⁼</span></code> when the value of <code><span class='Function'>F</span></code> in the expression is <code><span class='Function'>∨</span></code>, or <code><span class='Paren'>(</span><span class='Number'>1</span><span class='Function'>⊑∧</span><span class='Ligature'>‿</span><span class='Function'>∨</span><span class='Paren'>)</span><span class='Modifier'>⁼</span></code>.</p>
+<p>Failing to compute an inferred property for a function or array as it's created cannot cause an error. An error can only be caused when the missing inferred property is needed for a computation.</p>
<h2 id="identities">Identities</h2>
<p>When monadic Fold (<code><span class='Modifier'>´</span></code>) or Insert (<code><span class='Modifier'>˝</span></code>) is called on an array of length 0, BQN attempts to infer a right identity value for the function in order to determine the result. A right identity value for a dyadic function <code><span class='Function'>𝔽</span></code> is a value <code><span class='Value'>r</span></code> such that <code><span class='Value'>e</span><span class='Function'>≡</span><span class='Value'>e</span><span class='Function'>𝔽</span><span class='Value'>r</span></code> for any element <code><span class='Value'>e</span></code> in the domain. For such a value <code><span class='Value'>r</span></code>, the reduction <code><span class='Value'>r</span> <span class='Function'>𝔽</span><span class='Modifier'>´</span> <span class='Value'>l</span></code> is equivalent to <code><span class='Function'>𝔽</span><span class='Modifier'>´</span> <span class='Value'>l</span></code> for a non-empty list <code><span class='Value'>l</span></code>, because the first application <code><span class='Paren'>(</span><span class='Number'>¯1</span><span class='Function'>⊑</span><span class='Value'>l</span><span class='Paren'>)</span> <span class='Function'>𝔽</span> <span class='Value'>r</span></code> gives <code><span class='Number'>¯1</span><span class='Function'>⊑</span><span class='Value'>l</span></code>, which is the starting point when no initial value is given. It's thus reasonable to define <code><span class='Function'>𝔽</span><span class='Modifier'>´</span> <span class='Value'>l</span></code> to be <code><span class='Value'>r</span> <span class='Function'>𝔽</span><span class='Modifier'>´</span> <span class='Value'>l</span></code> for an empty list <code><span class='Value'>l</span></code> as well, giving a result <code><span class='Value'>r</span></code>.</p>
<p>For Fold, the result of <code><span class='Function'>𝔽</span><span class='Modifier'>´</span></code> on an empty list is defined to be a right identity value for the <em>range</em> of <code><span class='Function'>𝔽</span></code>, if exactly one such value exists. If an identity can't be proven to uniquely exist, then an error results.</p>